正交分頻多工 (orthogonal frequency division multiplexing ，簡稱 OFDM) 對於高位元傳輸速率的系統而言，是一種非常有效率的技術。高峰值對平均功率比 ( Peak-to-average power ratio )是OFDM 系統的嚴重缺點。為了解決這個問題，近年來已經發展出許多的峰值對平均功率比降低技術。在這些技術中，我們必須檢視 OFDM 訊號的峰值對平均功率比的分佈情形。因為實際的峰值對平均功率比是定義在連續性的OFDM傳輸訊號上，所以如果我們直接從經由奈奎斯特率( Nyquist rate )取樣的離散OFDM訊號上計算峰值對平均功率比，將會得到過度樂觀的結果。在傳統上， 倍數的補零超取樣 ( zero-padding oversampling ) 通常被使用來增加OFDM 訊號在時域上的解析度，如此超取樣訊號的峰值將會接近實際的峰值。當 倍數的補零超取樣技術被實現時，將需要花費 點的快速傅利葉反轉換( inverse fast Fourier transform ，簡稱IFFT )模組。 通常是四，但是在某些具有高次載波( subcarrier )數目的應用系統中，四倍數的補零超取樣仍然具有很高的計算複雜度。
在這篇論文中，我們提出一種低運算複雜度並且不需在頻域的OFDM訊號補零的峰值對平均功率比估測方式。這個估測演算法的基本觀念是來自於典型的上取樣( upsampling )系統（或是稱為內插器 ( interpolator )）並且是設計來近似四倍數的補零超取樣技術。當OFDM 訊號經過 點的快速傅利葉反轉換模組後，時域OFDM訊號的峰值對平均功率比會經由峰值搜尋及部分內插的程序得到。不論是在一般的OFDM訊號的峰值對平均功率比分佈表現或是用於特定應用中，譬如多重訊號表示( multiple signal representation )技術，和四倍數補零超取樣技術相比較，我們提出的峰值對平均功率估測方法都可以得到近似的估測結果必且具有較低的運算複雜度。

Orthogonal frequency division multiplexing (OFDM) is an efficient technique for high-bit-rate transmission. One major drawback of OFDM is the high peak-to-average power ratio (PAPR). To deal with this problem, many PAPR reduction schemes have been proposed. In these schemes, we have to exam the distribution of the PAPR value of an OFDM signal. Since the real PAPR value is defined on the continuous OFDM transmitted signal after the digital-to-analog converter (DAC) in the end of transmitter, we will get optimistic result if we calculate the PAPR value directly from the discrete OFDM signal sampled by Nyquist rate. Traditionally, -times zero-padding oversampling is used to increase the resolution of time-domained OFDM signal, thus the peak of oversampled signal is close to the real peak. It needs -points IFFT when -times zero-padding oversampling is implemented. is generally four, however, it still costs high computational complexity especially in certain application system with large subcarrer number .
In this thesis, we propose a low-complexity PAPR estimation method without padding zeros in the frequency-domained OFDM signal. This estimation algorithm is based on the concepts of typical upsampling system, called interpolator, and is designed to approximate the four-times zero-padding oversampling. After passing through the -points IFFT, the estimated PAPR value of the time-domained OFDM signal is obtained by Peak Search and Partial Interpolation process. The simulation results show that either in common PAPR distribution of an OFDM signal or in specific application such as multiple signal representation (MSR) techniques, the proposed PAPR estimation method could get well-approximated results and low computationally complexity compared with four-times zero-padding oversampling.

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